How do I Auto-Keyrame ONLY changed values?
Strictly spoken this is not possible. However, you can at least avoid channels being auto-keyed that do not have a keyframe on them yet.

So first, as suggested by josh, insert a single keyframe on a channel you'd like to animate, say Location Z. Then you need to switch the Active Keying Set to Available, and next to the Auto Keyframing dropdown enable the little button to the right with the keys:



Then only the available channel will be keyed, not all three of them. If however you also have a single keyframe on the rotation, that channel will also receive a keyframe, regardless of the value having changed or not.

The Graph Editor also offers a function that will remove any non-value-change keyframes using a threshold, Clean Keyframes. This way you can quickly get rid of duplicates and duplicates of same keyframes on channels, or even channels that did in fact never change their value using the Clean Channels operator: